I read it in the early 90s, might have been published late 80s in Canada. The story begins with a mysterious disk that appears between the sun and the Earth and starts an ice age which wipes out humanity except for a group that went deep underground and another that was on a space station. The disk disappears after a few hundred(?) years and most of the story is about the underground survivors, the terrible things that happened underground (executions of non-white non-Christians, generations of incest, dictatorship), and the rocky reunion with the survivors from space after the thaw, told from the POV of an underground survivor who became a historian. It ends with a meeting on the moon between the aliens who created the disk and the n-th generation human survivors, where we learn why the aliens did what they did and our ultimate response. :-)
"Central Heat" by David Dvorkin (1988).
I saw it as a sci-fi used paperback in a store in 1995(?). Protagonist starts off underground, rescued by the humans above (but loses a stalker girlfriend in the process). Eventually marries the leader's daughter, becoming the leader of the space-faring humans themselves, and ultimately betrays his wife in order to exact revenge on the aliens that hid the Sun from Earth and caused the near-genocide devastation.
The aliens turned out to be from a nearby star that were horrified by our early radio broadcasts that upset their strict caste system. Using a "quantum leap" form of faster-than-light communication and transport (progressively larger teleport jumps), they first transported the shield that cut off solar radiation from the Sun to Earth, along with a cryptic message telling humans "to know their place".
The story ends with the aliens coming to the Moon for the first contact with humans, but the protagonist double-crosses them and captures them for their starship technology with the intent of conquering and colonizing the alien homeworld as a replacement for making Earth uninhabitable.